Quantum dynamical semigroups for diffusion models with Hartree interaction [PDF]
, 2003 We consider a class of evolution equations in Lindblad form, which model the dynamics of dissipative quantum mechanical systems with mean-field interaction. Particularly, this class includes the so-called Quantum Fokker-Planck-Poisson model. The existence and uniqueness of global-in-time, mass preserving solutions is proved, thus establishing the ...
arxiv +1 more source
Strong convergence theorems for strongly monotone mappings in Banach spaces [PDF]
, 2020 Let $E$ be a uniformly smooth and uniformly convex real Banach space and $E^*$ be its dual space. Suppose $A : E\rightarrow E^*$ is bounded, strongly monotone and satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired by Alber [2], we introduce Lyapunov functions and use the new geometric properties of Banach spaces to show the ...
arxiv +1 more source
The generalized porous medium equation on graphs: existence and uniqueness of solutions with $\ell^1$ data [PDF]
arXiv, 2021 We study solutions of the generalized porous medium equation on infinite graphs. For nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild solutions on any graph. For changing sign integrable data, we show existence and uniqueness under extra assumptions such as local finiteness or a uniform lower bound on the node ...
arxiv
Real interpolation of functions with applications to accretive operators on Banach spaces [PDF]
arXiv, 2022 We study real interpolation, but instead of interpolating between Banach spaces, we interpolate between general functions taking values in $[0,\infty].$ We show the equivalence of the mean method and the $K$-method and apply the general theory to interpolation between the norm on a Banach space and the set norm associated with an m-accretive operator ...
arxiv
On quantitative metastability for accretive operators [PDF]
arXiv, 2022 Kohlenbach and the author have extracted a rate of metastability for approximate curves associated to continuous pseudocontractive self-mappings in Banach spaces which are uniformly convex and uniformly smooth, whose convergence is due to Reich. In this note, we show that this result may be extended to Reich's original convergence statement involving ...
arxiv
Existence and uniqueness for $p$-adic counterpart of the porous medium equation [PDF]
arXiv, 2023 We develop a theory of generalized solutions of the nonlinear evolution equations for complex-valued functions of a real positive time variable and $p$-adic spatial variable, which can be seen as non-Archimedean counterparts of the fractional porous medium equation.
arxiv
Alternative iterative methods for nonexpansive mappings, rates of convergence and application [PDF]
arXiv, 2009 Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such iterations using proof-theoretic techniques. Some applications of the convergence results are presented.
arxiv
Lyapunov Functionals and Local Dissipativity for the Vorticity Equation in L^p and Besov Spaces [PDF]
Differential and Integral Equations, Volume20, Number 5 (2007),
481- 498, 2008 In this paper we establish the local Lyapunov property of certain L^p and Besov norms of the vorticity fields. We have resolved in part, a certain open problem posed by Tosio Kato for the three dimensional Navier Stokes equation by studying the vorticity equation.
arxiv
Solution of variational inequality problems on fixed point sets of nonexpansive mappings using iterative methods [PDF]
arXiv, 2010 In this paper, we introduce new implicit and explicit iterative schemes which converge strongly to a unique solution of variational inequality problems for strongly accretive operators over a common fixed point set of finite family of nonexpansive mappings in $q$-uniformly smooth real Banach spaces.
arxiv
Hybrid Algorithm for Nonlinear Equilibrium, Variational Inequality and Fixed Point Problems [PDF]
Journal of Basic Physical Research, Vol. 7, N0.1, pp 1-17 (2017), 2020 In this paper, we introduce an iterative process which converges strongly to a common element of sets of solutions of finite family of generalized equilibrium problems, sets of fixed points of finite family of continuous relatively nonexpansive mappings and sets of zeros of finite family of $\gamma$-inverse strongly monotone mappings in Banach spaces ...
arxiv